To make a quad net with equal edge lengths (also known as a Chebyshev net), it is easier to approach by draping a full grid then cutting off the parts beyond the plane:
drape_sphere.gh (8.1 KB)
Cutting a flat mesh to a circle then anchoring the points around the boundary as you were doing will result in crumpling, because it prevents the angles from changing as they need to to form a smooth curved surface.